On the existence of periodic solutions to a p-Laplacian Allen-Cahn equation with Neumann boundary condition

This work is concerned with the periodic solution of a p-Laplacian Allen-Cahn equation with nonlocal terms associated with Neumann boundary conditions. Namely, the topological degree theorem is applied to prove the existence of a limit point to the auxiliary problem, which is also considered a nontrivial nonnegative time-periodic solution of the main studied problem. The results of this work can be extended to other similar equations with homogeneous Dirichlet or Neumann boundary conditions.